Deep learning models have revolutionized various domains, with Multi-Layer Perceptrons (MLPs) being a cornerstone for tasks like data regression and image classification. However, a recent study has introduced Kolmogorov-Arnold Networks (KANs) as promising alternatives to MLPs, leveraging activation functions placed on edges rather than nodes. This structural shift aligns KANs closely with the Kolmogorov-Arnold representation theorem, potentially enhancing both model accuracy and interpretability. In this study, we explore the efficacy of KANs in the context of data representation via autoencoders, comparing their performance with traditional Convolutional Neural Networks (CNNs) on the MNIST, SVHN, and CIFAR-10 datasets. Our results demonstrate that KAN-based autoencoders achieve competitive performance in terms of reconstruction accuracy, thereby suggesting their viability as effective tools in data analysis tasks.
Kolmogorov-Arnold networks for metal surface defect classification
AGH University of Krakow（克拉科夫AGH大学）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；University of Technology Sydney（悉尼科技大学）；Óbuda University（欧布达大学）；NASK National Research Institute（NASK国家研究院）
Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation
Indian Institute of Science Education and Research Mohali（印度科学教育与研究研究所莫哈利分校）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育与研究研究所蒂鲁文南特布勒姆分校）
PostHoc FREE Calibrating on Kolmogorov Arnold Networks
Institute for Clarity in Documentation（文献研究所）；Inria Paris-Rocquencourt（法国国家信息与自动化研究所巴黎-罗康校区）；Rajiv Gandhi University（拉吉夫·甘地大学）；Tsinghua University（清华大学）；Palmer Research Laboratories（帕尔默研究实验室）
A Practitioner's Guide to Kolmogorov-Arnold Networks
Department of Mathematics, Hong Kong Baptist University（香港 Baptist大学数学系）；Institution for Foundations of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Robotics and Technology of Computers Lab., Universidad de Sevilla（机器人与计算机技术实验室，塞维利亚大学）
QuKAN: A Quantum Circuit Born Machine approach to Quantum Kolmogorov Arnold Networks
Department of Computer Science and Research Initiative QC-AI, RPTU Kaiserslautern-Landau（计算机科学系和QC-AI研究计划，鲁尔-帕绍大学（RPTU）凯斯贝赫-劳恩道分校）；Embedded Intelligence, German Research Center for Artificial Intelligence (DFKI)（嵌入式智能，德国人工智能研究中心（DFKI））；Department of Physics, RPTU Kaiserslautern-Landau（物理系，鲁尔-帕绍大学（RPTU）凯斯贝赫-劳恩道分校）
本研究利用量子电路 Born 机（QCBM）在混合与全量子形式下实现了 KAN 架构，通过预训练残差函数发挥参数化量子电路的表示能力，验证了 QuKAN 架构的可行性、可解释性与性能。
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿科学研究所）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Department of Physics, Humboldt University Berlin（柏林洪堡大学物理系）；Research Institute of Intelligent Complex Systems, Fudan University（复旦大学智能复杂系统研究所）；School of Physics, University of Electronic Science and Technology of China（电子科技大学物理学院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（电子科技大学教育部量子物理与光子量子信息重点实验室）；Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（电子科技大学四川省非经典信息科学基础学科研究中心）
Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities
Skolkovo Institute of Science and Technology（斯克洛夫科学与技术研究所）；Southern University of Science and Technology（南方科技大学）；International Center for Mathematics（国际数学中心）；National Center for Applied Mathematics Shenzhen (NCAMS)（深圳应用数学中心）
Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks
College of Mechanical Engineering, Chongqing University of Technology（重庆理工大学机械工程学院）；Nagoya University（名古屋大学）；Faculty of Engineering, Yamaguchi University（山口大学工程学院）
Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)
Department of Materials Science and Engineering, Delft University of Technology（材料科学与工程系，代尔夫特理工大学）；Department of Biomechanical Engineering, Delft University of Technology（生物机械工程系，代尔夫特理工大学）
University of Twente（特文特大学）；Leiden University（莱顿大学）
There is a longstanding debate whether the Kolmogorov-Arnold representation theorem can explain the use of more than one hidden layer in neural networks. The Kolmogorov-Arnold representation decomposes a multivariate function into an interior and an outer function and therefore has indeed a similar structure as a neural network with two hidden layers. But there are distinctive differences. One of the main obstacles is that the outer function depends on the represented function and can be wildly varying even if the represented function is smooth. We derive modifications of the Kolmogorov-Arnold…
HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation
the Faculty of Electrical Engineering, Czestochowa University of Technology（捷斯托霍瓦技术大学电子工程系）；the Faculty of Mathematics and Computer Science, University of Lodz（罗兹大学数学与计算机科学系）；the Centre for Data Analysis, Modelling and Computational Sciences (CAMINO), University of Lodz（罗兹大学数据分析、建模与计算科学中心）
Columbia University（哥伦比亚大学）；National University of Singapore（新加坡国立大学）
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov--Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.
